1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328
|
*> \brief \b CLA_SYRCOND_C
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLA_SYRCOND_C + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_syrcond_c.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_syrcond_c.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_syrcond_c.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION CLA_SYRCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
* CAPPLY, INFO, WORK, RWORK )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* LOGICAL CAPPLY
* INTEGER N, LDA, LDAF, INFO
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
* REAL C( * ), RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLA_SYRCOND_C Computes the infinity norm condition number of
*> op(A) * inv(diag(C)) where C is a REAL vector.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order of the
*> matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the N-by-N matrix A
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is COMPLEX array, dimension (LDAF,N)
*> The block diagonal matrix D and the multipliers used to
*> obtain the factor U or L as computed by CSYTRF.
*> \endverbatim
*>
*> \param[in] LDAF
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges and the block structure of D
*> as determined by CSYTRF.
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is REAL array, dimension (N)
*> The vector C in the formula op(A) * inv(diag(C)).
*> \endverbatim
*>
*> \param[in] CAPPLY
*> \verbatim
*> CAPPLY is LOGICAL
*> If .TRUE. then access the vector C in the formula above.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: Successful exit.
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (2*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (N).
*> Workspace.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complexSYcomputational
*
* =====================================================================
REAL FUNCTION CLA_SYRCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
$ CAPPLY, INFO, WORK, RWORK )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
LOGICAL CAPPLY
INTEGER N, LDA, LDAF, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
REAL C( * ), RWORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER KASE
REAL AINVNM, ANORM, TMP
INTEGER I, J
LOGICAL UP, UPPER
COMPLEX ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLACN2, CSYTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function Definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
CLA_SYRCOND_C = 0.0E+0
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLA_SYRCOND_C', -INFO )
RETURN
END IF
UP = .FALSE.
IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
*
* Compute norm of op(A)*op2(C).
*
ANORM = 0.0E+0
IF ( UP ) THEN
DO I = 1, N
TMP = 0.0E+0
IF ( CAPPLY ) THEN
DO J = 1, I
TMP = TMP + CABS1( A( J, I ) ) / C( J )
END DO
DO J = I+1, N
TMP = TMP + CABS1( A( I, J ) ) / C( J )
END DO
ELSE
DO J = 1, I
TMP = TMP + CABS1( A( J, I ) )
END DO
DO J = I+1, N
TMP = TMP + CABS1( A( I, J ) )
END DO
END IF
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
ELSE
DO I = 1, N
TMP = 0.0E+0
IF ( CAPPLY ) THEN
DO J = 1, I
TMP = TMP + CABS1( A( I, J ) ) / C( J )
END DO
DO J = I+1, N
TMP = TMP + CABS1( A( J, I ) ) / C( J )
END DO
ELSE
DO J = 1, I
TMP = TMP + CABS1( A( I, J ) )
END DO
DO J = I+1, N
TMP = TMP + CABS1( A( J, I ) )
END DO
END IF
RWORK( I ) = TMP
ANORM = MAX( ANORM, TMP )
END DO
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 ) THEN
CLA_SYRCOND_C = 1.0E+0
RETURN
ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
RETURN
END IF
*
* Estimate the norm of inv(op(A)).
*
AINVNM = 0.0E+0
*
KASE = 0
10 CONTINUE
CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.2 ) THEN
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
*
IF ( UP ) THEN
CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
ELSE
CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
ENDIF
*
* Multiply by inv(C).
*
IF ( CAPPLY ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
ELSE
*
* Multiply by inv(C**T).
*
IF ( CAPPLY ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
*
IF ( UP ) THEN
CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
ELSE
CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
$ WORK, N, INFO )
END IF
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * RWORK( I )
END DO
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM .NE. 0.0E+0 )
$ CLA_SYRCOND_C = 1.0E+0 / AINVNM
*
RETURN
*
END
|